Two successive displacement vectors act on a particle: at north of east and at south…

PHYSICS · Subjective · AP · Physics 1: Algebra-based · Kinematics · Kinematics

Problem

Two successive displacement vectors act on a particle:

\mathbf{A}=10\,\text{m}

40^{\circ}

north of east and

\mathbf{B}=15\,\text{m}

30^{\circ}

south of east. The particle is then given a third displacement

\mathbf{C}

so that it finally reaches a point

20\,\text{m}

due north of the initial position. (a) Calculate the

x

- and

y

-components of

\mathbf{A}+\mathbf{B}

. (b) Hence find the magnitude and direction of

\mathbf{C}

required to reach the stated final position.